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 Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 773–785 (Mi semr951)

Geometry and topology

Connections of nonzero curvature on homogeneous spaces of unsolvable transformations groups

N. P. Mozhey

Belarusian State University of Informatics and Radioelectronics, P. Brovki Street, 6, 220013, Minsk, Belarus

Abstract: The purpose of the work is the local classification of three-dimensional homogeneous spaces, admits invariant affine connections nonzero curvature only, description of the connections on those spaces together with their curvature and torsion tensors, holonomy algebras. We have concerned the case of the unsolvable Lie group of transformations. The local classification of homogeneous spaces is equivalent to the description of the effective pairs of Lie algebras. Studies are based on the use of properties of the Lie algebras, Lie groups and homogeneous spaces and they mainly have local character.

Keywords: affine connection, transformation group, homogeneous space, curvature tensor.

DOI: https://doi.org/10.17377/semi.2018.15.063

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Document Type: Article
UDC: 514.76
MSC: 53B05
Received May 29, 2017, published July 18, 2018

Citation: N. P. Mozhey, “Connections of nonzero curvature on homogeneous spaces of unsolvable transformations groups”, Sib. Èlektron. Mat. Izv., 15 (2018), 773–785

Citation in format AMSBIB
\Bibitem{Moz18} \by N.~P.~Mozhey \paper Connections of nonzero curvature on homogeneous spaces of unsolvable transformations groups \jour Sib. \Elektron. Mat. Izv. \yr 2018 \vol 15 \pages 773--785 \mathnet{http://mi.mathnet.ru/semr951} \crossref{https://doi.org/10.17377/semi.2018.15.063} `